Partition of graphs with maximum degree ratio
Résumé
Given a graph and a non trivial partition (V1,V2) of its vertices, the satisfaction of a vertex v of Vi, i=1,2 is the ratio between the size of its closed neighborhood in Vi and the total size of its closed neighborhood. The worst ratio over all the vertices defines the quality of the partition. We define q(G) the degree ratio of a graph as the maximum of the worst ratio over all the non trivial partitions. We give bounds and exact values of q(G) for some classes of graphs. We also show some complexity results.